Liquid-gas phase transition in the canonical ensemble of asymmetric nuclear matter

New calculus of the liquid-gas phase transition is developed for the canonical ensemble of asymmetric nuclear matter. In contrast to the familiar geometrical construction, the pressure and the chemical potentials are determined for de…nite values of the baryon densities of proton and neutron and the temperature. Because the derivatives of chemical potentials by pressure have discontinuities at the ends of the phase transition, we conclude against the preceding works that the phase transition is the …rst order. Due to the …eld-dependent meson-nucleon coupling constants in our relativistic mean-…eld model of nuclear matter, the section of binodal surface has no critical point. The appearance of the retrograde condensation is also proved. The liquid-gas phase transition in warm nuclear matter [1,2] is a recent topic in nuclear physics. It is experimentally investigated [3,4] in the multifragmentation reactions of heavy ions. The nuclear matter produced in the reaction is charge asymmetric. It is a binary system that has two independent chemical potentials of proton and neutron. Based on the Gibbs condition in the phase equilibrium, both the chemical potentials in gaseous and liquid phases are equilibrated. Reference [5] determined them in terms of the geometrical construction, which was also used in the other works [6-9] of the liquid-gas phase transition in asymmetric nuclear matter. In the geometrical construction, the chemical potentials are determined for a …xed value of the pressure and the asymmetry of nuclear matter. However, the object is neither a canonical nor a grand-canonical ensemble. In contrast to the condensed matter physics we cannot press nuclear matter under a de…nite pressure in nuclear experiments. In this point of view, the geometrical construction is not physically consistent with the liquid-gas phase transition in nuclear multifragmentation reactions. On the other hand, another strategy is proposed recently in Ref. [10], which considers a neutron grandcanonical but proton canonical ensemble. The investigation of phase equilibrium is much easier than the geometrical construction because the Maxwell construction is applicable. Nevertheless, the total system in Ref. [10] is neither canonical nor grand-canonical yet. In the present paper we investigate for the …rst time the liquid-gas phase transition in the canonical ensemble of binary nuclear system. We are based on the relativistic mean…eld (RMF) model of asymmetric nuclear matter developed in Refs. [11] and [12]. The